Interference patterns for measuring test object surface topologies are generally captured as overlapping images of the test surface and a reference surface illuminated by different portions of a common coherent beam of light. Within the coherence length of the two beam portions, the intensity of each pixel within the interference pattern is subject to variation within a cycle of constructive and destructive depending upon the local phases of the beam portions forming the overlapping images.
If one beam portion is required to travel an optical path length slightly more or less than the other beam portion, the coherent wave forms of the two beam portions can arrive at the image plane out of phase with one another. The pixels are the brightest when formed by beam portions that constructively interfere by traveling equal optical path lengths or optical path lengths that differ by an integer multiple of the common wavelength of the beam portions. The pixels are darkest when formed by beam portions that destructively interfere by traveling optical path lengths that differ by one-half of the common wavelength or an integer multiple of the wavelength more so that the beam portions remain 180 degrees out of phase. Thus, pixel intensity can be used as a measure of the local phase difference between the object and reference beams, and the phase difference, as an angular portion of a 2π wave cycle can be converted into a fractional portion of the beam wavelength, as a variation in distance.
Since each cycle of constructive and destructive interference produces a repetitive pattern of pixel intensity variation, the intensity values of individual pixels within an interference pattern provide measurements limited to one wavelength of the measuring beam, which limit is referred to as an ambiguity interval. The ambiguity interval for measuring surface topographies expressed as a relative height variation between test and reference surfaces is generally limited to one-half wavelength because the height variation measured under reflection doubles the optical path length difference between beam portions. Test surfaces that vary gradually in height by more than one-half wavelength can still be measured by a procedure referred to a “phase unwrapping” by assuming that the variation between adjacent pixels is within the one-half wavelength ambiguity interval. Nonetheless, with ambiguity intervals of less than 400 nanometers for measuring beams within the visible range, only very smooth surfaces qualify for this sort of measurement.
The conversion of pixel intensity to a phase difference between beam portions can be problematic because pixel intensity is subject to a number of influences beyond interference. For example, pixel intensity can vary over the imaging field because of illuminating conditions or even the local reflectivity of the test surface. Phase shifting interferometry has been developed to overcome this problem by forming a succession of interference patterns at incrementally varied optical path length differences to shift each pixel through a cycle of constructive and destructive interference. Thus, the intensity of each pixel can be compared to the range of intensity variation within its own cycle of constructive and destructive interference. Data from as few as three incrementally phase shifted interference patterns can be used to convert pixel intensity into a useable measure of height variation.
Test surfaces with topography variations beyond optical quality, such as machined metal surfaces, are generally not measurable by conventional interferometric methods. For many such surfaces, the pixel-to-pixel intensity variation is so high that interference fringes are not visible within the interference patterns. Phase unwrapping cannot be used to relate the height of pixels to one another across a test surface because the pixel-to-pixel variation between adjacent pixels can exceed the ambiguity interval.
Frequency shifting interferometry is one of the alternative interferometric methods available for measuring “rough” or discontinuous test surfaces, defined as surfaces with adjacent pixel variations exceeding the usual ambiguity interval of conventional interferometers. A sequence of interference patterns are captured by varying the measuring beam frequency between each of the patterns. The rate at which individual pixels vary in intensity between constructive and destructive interference with the variation in beam frequency is known to be a function of the optical path length difference between the object and reference beam portions. The cumulative effect of a change in wavelength is greater over a greater optical path length difference.
Whether the beam frequency is varied incrementally between captured interference frames or the beam frequency is varied continuously and the interference frames are sampled incrementally, the beam frequency difference between the captured interference frames establishes a synthetic wavelength corresponding to an optical path length difference over which a pixel undergoes a single cycle of constructive and destructive interference. The synthetic wavelength, which can be defined as the speed of light divided by the incremental change in beam frequency, can be much longer than the wavelength of the measuring beam and can provide an expanded ambiguity interval.
Larger synthetic wavelengths are preferred for expanding the range of measurement (i.e., increasing the ambiguity interval) and a large number of sample interference frames (i.e., the number of incremental beam frequency steps captured in interference patterns) are preferred for improving the resolution of the measurement (i.e., the smallest height differences that can be discerned). However, together, the size frequency step and the number of frequency steps can be limited by the tunable range of the light source, usually a tunable laser source. Increasing the number of frequency steps increases both the time to capture the interference patterns and the time required to process the captured data.
Test objects with discontinuous surfaces or surfaces that are offset from one another can exceed even the enlarged ambiguity interval of frequency shifting interferometers. Although the offset surfaces can be separately measured, an additional measurement can be required to relate the offset surfaces to each other. The separate measurements of the surfaces and the additional measurement between surfaces can be time consuming and difficult to relate accurately to one another for providing an overall measurement of the test surfaces against a common datum.